exclude product with available tag

Question

You can setup a tax_query with the NOT IN operator.

WP_Query( array(
    'post_type' => 'product',
    'posts_per_page' => 500,
    'tax_query' => array(
        'relation' => 'AND'
        array(
            'taxonomy'  => 'product_cat',
            'field'     => 'slug',
            'terms'     => array( 'cars' ),
        ),
        array(
            'taxonomy'  => 'product_tag',
            'field'     => 'slug',
            'terms'     => array( 'whatever_tag_i_dont_need' ),
            'operator'  => 'NOT IN',
        ),
    ),
) )

The above will request all posts in assigned to term cars that don’t have any tags with the slug whatever_tag_i_dont_need. There’s other comparison operator too. For more information please reference the docs below:

https://developer.wordpress.org/reference/classes/wp_query/#taxonomy-parameters